( H5* 5 > 
j. in jEquatione x 3 = 63 x 1 + 9967% * '+ 995 * 705 > 
erk p = 21, q = — ^ r = 603x680 5 8c Binomn 
fo 3 .ao + ■/_ Radix Cubica eft 
182 4- V — Igitur x = 21 4 36b = 387 , 8c 
3 3 
x = 21 — 183 4 ( V 529 )23 = — 139. yel 185. 
Nec fecus in caeteris procedendum • Inveftigstur autem 
Theorem* ad modum fequentem. Pono %ua(ionis cu- 
lufdam Cubicae Radicem z = a 4 b, 8c cubice multi- 
plicando proveniet z5 = ( a 5 4- 3 a" b 4- 3 a b r b> - J 
a j 4 3 ab *T4~b 4 bJ. Jam loco ipfius a+b valo- 
rem eius z fubftituendo, fiet z 3 = 3 a b z 4 a 3 4 b?, quae 
eft iEquatio Cubica ex Radies z = a 4 b conftrucra, cui 
terminus fecundus deeft. Ut h$c vero ad formam magis 
commodam magifq^ concinnam revocenter, futno ^qua- 
tioneni = 3 q z + 2 r, qox pofthac ipfius z s = 3 a b z 
4. a s 4 b3 vices gerat. Igitur tranfmutatione hujus in 
illam, fiet primo 3 q = 3 a b, five q 3 = as b 3 ; 8c fe- 
cnndb 2 r =4 a 3 4 b 3 , five 2 ra 3 =(a 6 4 a 3 b 3 = )a g 4 q 3 . 
Et foluca hac tequadone quadratlca^rit a’ = r 4 V r z ■ — ■ q 3 , 
8c hinc b 3 = (2 r — as = ) r — 4 r* — q 3 : Atqne igi- 
s 
tur tandem a — V r 4 ^ r * - q 3 _Sc b == / r — V — q 3 . 
Et propterea in iEquati°ne Cubica 2 } — 3 q z 4 2 r crit 
Radix z=(a 4 b=)^r* + ft 3 . + ^ r *— v T-Z q? 
At verb hsec Radix reverd triplex eft, pro triplici va- 
lore quern induere poteft 8c y r 4 ^ r 1 — qs 8c 
V r . — V r 1 — q 3 . Cujufvis enim quantitafis Radix Cu- 
bica triplex erit, 8c ipfius llnitatis Radix Cubica vel 
eft 
